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Standard XII

Physics

Thermal Resistance

A composite r...

Question

A composite rod made of three rods of equal length and cross-section as shown in the fig. The thermal conductivities of the materials of the rods are $K / 2$ , $5 K$ and $K$ respectively. The end $A$ and end $B$ are at constant temperatures. All heat entering the face $A$ goes out of the end $B$ . Assuming no loss of heat from the sides of the bar. The effective thermal conductivity of the bar is :

\frac{15 K}{16}

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\frac{6 K}{13}

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\frac{5 K}{16}

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\frac{2 K}{13}

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Solution

The correct option is D $\frac{15 K}{16}$
by given concept
$\frac{3 l}{K} = \frac{l}{k / 2} + \frac{l}{5 k} + \frac{l}{k}$
$\frac{3 l}{K} = \frac{2 l}{k} + \frac{l}{5 k} + \frac{l}{k} = \frac{10 l + l + 5 l}{5 k} = \frac{16 l}{5 k}$
$K = \frac{15 k}{16}$

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The correct option is D 15K16by given concept3lK=lk/2+l5k+lk3lK=2lk+l5k+lk=10l+l+5l5k=16l5kK=15k16

The correct option is D $\frac{15 K}{16}$
by given concept
$\frac{3 l}{K} = \frac{l}{k / 2} + \frac{l}{5 k} + \frac{l}{k}$
$\frac{3 l}{K} = \frac{2 l}{k} + \frac{l}{5 k} + \frac{l}{k} = \frac{10 l + l + 5 l}{5 k} = \frac{16 l}{5 k}$
$K = \frac{15 k}{16}$